In the scope of (infinite) lattices, the transmitted information rate and the signal-to-noise ratio based on the second-order moment are pointless. Poltyrev introduced the generalized
capacity [1]} [2]}, the analog of Shannon
capacity for lattices. The Poltyrev limit corresponds to a noise variance of
\(\sigma ^2_{max}=\operatornamewithlimits{Vol}(\Lambda )^{\frac{2}{n}}/(2 \pi e)\) .
The point error rate on the Gaussian channel is therefore evaluated
with respect to the distance to Poltyrev limit, also called the volume-to-noise ratio (VNR) [2]}, i.e.
\(\Delta = \frac{\sigma ^2_{max}}{\sigma ^2}.\) 
